code: def test_ard(self):
      x1 = torch.tensor([[4, 2], [3, 1], [8, 5]], dtype=torch.float)
      x2 = torch.tensor([[4, 2], [3, 0], [4, 4]], dtype=torch.float)
      lengthscales = torch.tensor([1, 2], dtype=torch.float).view(
          1, 1, 2
      )
  
      kernel = CategoricalKernel(ard_num_dims=2)
      kernel.initialize(lengthscale=lengthscales)
      kernel.eval()
  
      sc_dists = x1.unsqueeze(-2) != x2.unsqueeze(-3)
      sc_dists = sc_dists / lengthscales
      actual = torch.exp(-sc_dists.mean(-1))
      res = kernel(x1, x2).to_dense()
      self.assertAllClose(res, actual)
  
      # diag
      res = kernel(x1, x2).diagonal()
      actual = torch.diagonal(actual, dim1=-1, dim2=-2)
      self.assertAllClose(res, actual)
  
      # batch_dims
      actual = torch.exp(-sc_dists).transpose(-1, -3)
      res = kernel(x1, x2, last_dim_is_batch=True).to_dense()
      self.assertAllClose(res, actual)
  
      # batch_dims + diag
      res = kernel(x1, x2, last_dim_is_batch=True).diagonal()
      self.assertAllClose(res, torch.diagonal(actual, dim1=-1, dim2=-2))
  
file_path: botorch/test/models/kernels/test_categorical.py
imports: import torch
  from botorch.models.kernels.categorical import CategoricalKernel
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.test.base_kernel_test_case import BaseKernelTestCase
label_desc: Use image node_id 9 for calling the TestCategoricalKernel obj's underlying member method code with example usage: obj.test_ard() without return types